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Summary: Stratified Sampling of Spherical Triangles
James Arvo
Program of Computer Graphics \Lambda
Cornell University
Abstract
We present an algorithm for generating uniformly dis
tributed random samples from arbitrary spherical triangles.
The algorithm is based on a transformation of the unit
square and easily accommodates stratified sampling, an ef
fective means of reducing variance. With the new algorithm
it is straightforward to perform stratified sampling of the
solid angle subtended by an arbitrary polygon; this is a fun
damental operation in image synthesis which has not been
addressed in the Monte Carlo literature. We derive the re
quired transformation using elementary spherical trigonom
etry and provide the complete sampling algorithm.
CR Categories and Subject Descriptors: I.3.5 [Com
putational Geometry and Object Modeling]: Geometric Al
gorithms.
Additional Key Words and Phrases: Monte Carlo, solid
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